Skip to main content
SpringerLink
Log in
Book cover

Chaotic Processes in the Geological Sciences pp 141–173Cite as

Vigorous Motions in Magma Chambers and Lava Lakes

  • Conference paper

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 41))

Abstract

Magma chambers and lava lakes are storage reservoirs of molten rock, which gradually cools and solidifies after emplacement. The molten rock is a multicomponent silicate melt that crystallizes to form a solid whose components differ locally from those of the original melt. This difference in composition can drive strong convective motions in the melt and cause large-scale zonation of minerals.

This paper considers a series of general, one-dimensional problems in which a layer of a one- or two-component melt is cooled from above. We describe the fundamental fluid-mechanical processes involved, which include: the influence of compositional effects on the solidification; the formation of mushy layers — regions in which fluid and solid co-exist; and the kinetic effects associated with disequilibrium thermodynamics. The solutions of the resultant mathematical models are compared with data from laboratory experiments using aqueous solutions. The agreement between the two sets of results is shown to be very good. Calculations using the simple, geologically oriented, two- component anorthite-diopside system are presented and their geological interpretation discussed briefly.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Crank, Free- and Moving-Dovndary Problems, Clarendon Press, Oxford, 1984.

    Google Scholar 

  2. J. M. Hill, One-dimensional Stefan Problems: An Introduction, Longman, Harlow, 1987.

    Google Scholar 

  3. J. S. Turner, H. E. Huppert and R. S. J. Sparks, Komatiites II: Experimental and theoretical investigations of post-emplacement cooling and crystallization, J. Petrol., 27 (1986), pp. 397–437.

    Google Scholar 

  4. R. C. Kerr, A. W. Woods, M. G. Worster and H. E. Huppert, Disequilibrium and macrosegregation during solidificaUon of a binary melt, Nature 340 (1989), PP. 357–362.

    Article  ADS  Google Scholar 

  5. R. C. Kerr, A. W. Woods, M. G. Worster and H. E. Huppert, Soldification of an alloy cooled from above. Part I Equilibrium growth, J. Fluid Mech., 216 (1990), pp.323–342.

    Article  ADS  Google Scholar 

  6. R.C. Kerr, A.W. Woods, M.G. Worster and H.E. Huppert, Solidification of an alloy cooled from above. Part II Non-equilibrium interfacial kinetics, J. Fluid Mech., 217 (1990), pp.331–348.

    Article  ADS  MATH  Google Scholar 

  7. J. S. Turner, Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, 1979.

    MATH  Google Scholar 

  8. T. L. Wright and R.T. Okamura, Cooling and crystallization of tholeiitic basalt, 1965 Makaopuhi lava lake, Hawaii, U.S. Geol. Survey Prof, paper, 1004 (1977), 78pp.

    Google Scholar 

  9. T. L. Wright, D. L. Peck and H. R. Shaw, Kilauea lava lakes: natural laboratories of study of cooling, crysiallization and differentiation of basaltic magma in The Geophysics of the Pacific Ocean Basin and its Margin (G. H. Sutton, M. H. Manghnani and R. Moberly, Eds) American Geophysical Union, Washington D.C. (1976), pp. 375–390

    Google Scholar 

  10. H.E. Huppert and M. G. Worster, Dynamic solidification of a binary melt. Nature, 314 (1985), pp. 703–707.

    Article  ADS  Google Scholar 

  11. M.G. Worster, Solidification of an alloy from, a cooled boundary, J. Fluid Mech., 167 (1986), pp. 481–501.

    Article  ADS  MATH  Google Scholar 

  12. M.G. Worster, Natural convection in a mushy layer, J. Fluid Mech., 224 (1991), pp. 335–359.

    Article  ADS  MATH  Google Scholar 

  13. G. Brandéis and B. D. Marsh, The convective liquidus in a solidifying magma chamber: a fluid dynamic investigation, Nature, 339 (1989), pp.613–616.

    Article  ADS  Google Scholar 

  14. W. Kurz and D. J. Fisher, Fundamentals of Solidification, Trans. Tech. Publications, Aedermannsdorf (1986)

    Google Scholar 

  15. R.J. Kirkpatrick, Crystal growth from, the melt: a review, American Mineralogist, 60 (1975), pp.798–814.

    Google Scholar 

  16. R.C. Kerr, A.W. Woods, M.G. Worster and H.E. Huppert, Solidification of an alloy cooled from above. Part III Stratification of the solid, J. Fluid Mech., 218 (1990), pp.337–354.

    Article  ADS  MATH  Google Scholar 

  17. M.P. Ryan, R.Y. Koyanagi and R.S. Fiske, Modelling the three-dimensional structure of macroscopic magma transport, systems: Application to Kilauea Volcano, Hawaii, J. Geophys. Res., 86 (1981), pp.7111–7129.

    Article  ADS  Google Scholar 

  18. R.S. Detrick, P. Buhl, E. Era, J Mutter, J. Orcutt, J. Madsen and T. Brocher, Multi-channel seismic imaging of a crustal magma chamber along the East Pacific Rise, Nature, 326 (1987), pp.34–41.

    Article  ADS  Google Scholar 

  19. K.C. Macdonald, Anatomy of the magma reservoir. Nature, 339 (1989), PP.178–179.

    Article  ADS  Google Scholar 

  20. M.S. Burnett, D.W. Caress and J.A. Orcutt, Tomographic image of the magma chamber at 12° 50’ N on the East Pacific Rise, Nature, 339 (1989), pp.206–208.

    Article  ADS  Google Scholar 

  21. G.M. Kent, A.J. Harding and J.A. Orcutt, Evidence for a smaller magma chamber beneath the East Pacific Rise at 9° 30’ N Nature, 344 (1990), pp.650–653.

    Article  ADS  Google Scholar 

  22. C. Jaupart, G. Brandéis and C. J. Allegre, Stagnant layers at the bottom of convecting magma chambers, Nature, 308 (1984), pp.535–538.

    Article  ADS  Google Scholar 

  23. C. Jaupart and G. Brandéis, The stagnant bottom layer of convecting magma chambers. Earth and Planet. Sci. Lett., 80 (1986) pp.183–199.

    Article  ADS  Google Scholar 

  24. D.F. Neill, R. Hon and A. Navrotsky, The igneous system CaMgSi 2 O 6— CaAl 2 Si 2 O 6 — NaAl 2 Si 2 O 2 : variations on a classic theme by Bowen, in Physics of Magmatic Processes (RB. Margraves, Ed), Princeton University Press, New Jersey, 1980.

    Google Scholar 

  25. R.J. Kirkpatrick, G.R. Robinson and J.F. Hays, Kinetics of crystal growth from silicate melts: anorthite and diopside, J. Geophys. Res., (1976), pp.5715–5720.

    Google Scholar 

  26. H.E. Huppert, J.S. Turner and R.S.J. Sparks, Replenished magma chambers: effects of compositional zonation and input rates, Earth and Planet. Sci. Lett., 57 (1982), pp.345–357.

    Article  ADS  Google Scholar 

  27. M.G. Worster, H.E. Huppert and R.S.J. Sparks, Convection and crystallization in magma cooled from above, Earth and Planet. Sci. Lett., 101 (1990), pp. 78–89.

    Article  ADS  Google Scholar 

  28. R.J. Kirkpatrick, Kinetics of crystal growth in the system CaMgSi 2 O 2 — CaAl 2 SiO 6, American Journal of Science, 274 (1974), pp.215–242.

    Article  Google Scholar 

  29. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Cambridge University Press, Cambridge, 1959.

    Google Scholar 

  30. B. D. Marsh, On convective style and vigor in sheet-like magma chambers, Journal of Petrology, 30 (1989), pp.479–530.

    Google Scholar 

  31. H.E. Huppert, The intrusion of fluid mechanics into geology, J. Fluid Mech., 173 (1986), pp.557–594.

    Article  ADS  Google Scholar 

  32. H.E. Huppert, The fluid mechanics of solidification, J. Fluid Mech., 212 (1990) pp.209–240.

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Geophysics, University of Cambridge, 20 Silver Street, CB3 9EW, Cambridge, UK

    Herbert E. Huppert

  2. Department of Engineering Sciences & Applied Mathematics, and Department of Chemical Engineering, Northwestern University, 60208, Evanston, Illinois, USA

    M. Grae Worster

Authors
  1. Herbert E. Huppert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Grae Worster
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Minnesota Supercomputer Institute, Army High Performance Computing and Research Center, University of Minnesota, 55415, Minneapolis, MN, USA

    David A. Yuen

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Huppert, H.E., Worster, M.G. (1992). Vigorous Motions in Magma Chambers and Lava Lakes. In: Yuen, D.A. (eds) Chaotic Processes in the Geological Sciences. The IMA Volumes in Mathematics and its Applications, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0643-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0643-6_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-0645-0

  • Online ISBN: 978-1-4684-0643-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation